IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2205.03852.html
   My bibliography  Save this paper

Randomized geometric tools for anomaly detection in stock markets

Author

Listed:
  • Cyril Bachelard
  • Apostolos Chalkis
  • Vissarion Fisikopoulos
  • Elias Tsigaridas

Abstract

We propose novel randomized geometric tools to detect low-volatility anomalies in stock markets; a principal problem in financial economics. Our modeling of the (detection) problem results in sampling and estimating the (relative) volume of geodesically non-convex and non-connected spherical patches that arise by intersecting a non-standard simplex with a sphere. To sample, we introduce two novel Markov Chain Monte Carlo (MCMC) algorithms that exploit the geometry of the problem and employ state-of-the-art continuous geometric random walks (such as Billiard walk and Hit-and-Run) adapted on spherical patches. To our knowledge, this is the first geometric formulation and MCMC-based analysis of the volatility puzzle in stock markets. We have implemented our algorithms in C++ (along with an R interface) and we illustrate the power of our approach by performing extensive experiments on real data. Our analyses provide accurate detection and new insights into the distribution of portfolios' performance characteristics. Moreover, we use our tools to show that classical methods for low-volatility anomaly detection in finance form bad proxies that could lead to misleading or inaccurate results.

Suggested Citation

  • Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2022. "Randomized geometric tools for anomaly detection in stock markets," Papers 2205.03852, arXiv.org, revised May 2022.
  • Handle: RePEc:arx:papers:2205.03852
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2205.03852
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    2. Simon Byrne & Mark Girolami, 2013. "Geodesic Monte Carlo on Embedded Manifolds," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 825-845, December.
    3. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, December.
    4. Cule, Madeleine & Gramacy, Robert B. & Samworth, Richard, 2009. "LogConcDEAD: An R Package for Maximum Likelihood Estimation of a Multivariate Log-Concave Density," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i02).
    5. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    6. Madeleine Cule & Richard Samworth & Michael Stewart, 2010. "Maximum likelihood estimation of a multi‐dimensional log‐concave density," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 545-607, November.
    7. Ledoit, Oliver & Wolf, Michael, 2008. "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 850-859, December.
    8. Asness, Cliff & Frazzini, Andrea & Gormsen, Niels Joachim & Pedersen, Lasse Heje, 2020. "Betting against correlation: Testing theories of the low-risk effect," Journal of Financial Economics, Elsevier, vol. 135(3), pages 629-652.
    9. Frazzini, Andrea & Pedersen, Lasse Heje, 2014. "Betting against beta," Journal of Financial Economics, Elsevier, vol. 111(1), pages 1-25.
    10. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    11. Liu, Jianan & Stambaugh, Robert F. & Yuan, Yu, 2018. "Absolving beta of volatility’s effects," Journal of Financial Economics, Elsevier, vol. 128(1), pages 1-15.
    12. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
    13. Gryazina, Elena & Polyak, Boris, 2014. "Random sampling: Billiard Walk algorithm," European Journal of Operational Research, Elsevier, vol. 238(2), pages 497-504.
    14. Carhart, Mark M, 1997. "On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    15. Blitz, David & Pang, Juan & van Vliet, Pim, 2013. "The volatility effect in emerging markets," Emerging Markets Review, Elsevier, vol. 16(C), pages 31-45.
    16. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    17. Claude J. P. Bélisle & H. Edwin Romeijn & Robert L. Smith, 1993. "Hit-and-Run Algorithms for Generating Multivariate Distributions," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 255-266, May.
    18. A. B. Dieker & Santosh S. Vempala, 2015. "Stochastic Billiards for Sampling from the Boundary of a Convex Set," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 888-901, October.
    19. Haugen, Robert A. & Heins, A. James, 1975. "Risk and the Rate of Return on Financial Assets: Some Old Wine in New Bottles," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(5), pages 775-784, December.
    20. Banz, Rolf W., 1981. "The relationship between return and market value of common stocks," Journal of Financial Economics, Elsevier, vol. 9(1), pages 3-18, March.
    21. Jegadeesh, Narasimhan & Titman, Sheridan, 1993. "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency," Journal of Finance, American Finance Association, vol. 48(1), pages 65-91, March.
    22. Blitz, D.C. & van Vliet, P., 2007. "The Volatility Effect: Lower Risk without Lower Return," ERIM Report Series Research in Management ERS-2007-044-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2023. "Randomized geometric tools for anomaly detection in stock markets," Post-Print hal-04223511, HAL.
    2. Bradrania, Reza & Veron, Jose Francisco & Wu, Winston, 2023. "The beta anomaly and the quality effect in international stock markets," Journal of Behavioral and Experimental Finance, Elsevier, vol. 38(C).
    3. Adam Zaremba & Jacob Koby Shemer, 2018. "Price-Based Investment Strategies," Springer Books, Springer, number 978-3-319-91530-2, February.
    4. Cyril Bachelard & Apostolos Chalkis & Vissarion Fisikopoulos & Elias Tsigaridas, 2024. "Randomized Control in Performance Analysis and Empirical Asset Pricing," Papers 2403.00009, arXiv.org.
    5. Bradrania, Reza & Veron, Jose Francisco, 2023. "The beta anomaly in the Australian stock market and the lottery demand," Pacific-Basin Finance Journal, Elsevier, vol. 77(C).
    6. Hanauer, Matthias X. & Lauterbach, Jochim G., 2019. "The cross-section of emerging market stock returns," Emerging Markets Review, Elsevier, vol. 38(C), pages 265-286.
    7. Joshua Traut, 2023. "What we know about the low-risk anomaly: a literature review," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(3), pages 297-324, September.
    8. Shiyang Huang & Xin Liu & Dong Lou & Christopher Polk, 2024. "The Booms and Busts of Beta Arbitrage," Management Science, INFORMS, vol. 70(8), pages 5367-5385, August.
    9. Flögel, Volker & Schlag, Christian & Zunft, Claudia, 2022. "Momentum-Managed Equity Factors," Journal of Banking & Finance, Elsevier, vol. 137(C).
    10. Sebastien Valeyre & Sofiane Aboura & Denis Grebenkov, 2019. "The Reactive Beta Model," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 42(1), pages 71-113, March.
    11. Flögel, Volker & Schlag, Christian & Zunft, Claudia, 2021. "Momentum-managed equity factors," SAFE Working Paper Series 317, Leibniz Institute for Financial Research SAFE.
    12. Asgar Ali & K. N. Badhani, 2021. "Beta-Anomaly: Evidence from the Indian Equity Market," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(1), pages 55-78, March.
    13. Sehgal, Sanjay & Rakhyani, Sarika & Deisting, Florent, 2022. "Does betting against beta strategy work in major Asian Markets?," Pacific-Basin Finance Journal, Elsevier, vol. 75(C).
    14. Han, Xing & Li, Kai & Li, Youwei, 2020. "Investor overconfidence and the security market line: New evidence from China," Journal of Economic Dynamics and Control, Elsevier, vol. 117(C).
    15. Massimo Guidolin & Manuela Pedio & Dimos Andronoudis, 2019. "How Smart is the Real Estate Smart Beta? Evidence from Optimal Style Factor Strategies for REITs," BAFFI CAREFIN Working Papers 19117, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    16. Stephen A. Gorman & Frank J. Fabozzi, 2021. "The ABC’s of the alternative risk premium: academic roots," Journal of Asset Management, Palgrave Macmillan, vol. 22(6), pages 405-436, October.
    17. David Blitz & Matthias X. Hanauer & Pim Vliet, 2021. "The Volatility Effect in China," Journal of Asset Management, Palgrave Macmillan, vol. 22(5), pages 338-349, September.
    18. Cakici, Nusret & Zaremba, Adam, 2022. "Salience theory and the cross-section of stock returns: International and further evidence," Journal of Financial Economics, Elsevier, vol. 146(2), pages 689-725.
    19. Poon, Percy & Yao, Tong & Zhang, Andrew (Jianzhong), 2022. "The alphas of beta and idiosyncratic volatility," Journal of Financial Markets, Elsevier, vol. 61(C).
    20. Sawaliya, Priya & Sinha, Pankaj, 2018. "Behaviour of asset pricing models in pre and post-recession period: an evidence from India," MPRA Paper 93084, University Library of Munich, Germany, revised 22 Jan 2019.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2205.03852. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.